Wallboxes are usually for charging in the local garage, as well as in parking garages or for example employer. A wallboxing is not something highly complex, wallboxes are just safe power outlets designed to charge the currents to the car without the user needing to know how exactly it works. They also check before and during each charging process that both the car and the cable are fine, as well as other peripheral conditions. They make sure that you can not do anything wrong when charging.
In addition, more expensive wallboxes can, for example, specifically charge the car at night with favorable night-time electricity or with the right now available power delivered by your photovoltaic system.
All charging stations are standardized and basically every car can be charged at every charging station. Just because the wallbox is from Mercedes, that does not mean that not even a BMW or Kia can charge there. In addition, all Typ2 based charging stations secure the charging cable, so it's locked and can not be removed by strangers.
Note: Tesla still is using there own standard in the US
In addition to Wallboxes, there are also so-called emergency cable for charging to ordinary 110V-220V sockets, these allow it to charge at any outlet. So you can, for example, quite conveniently and easily charge at your friends place while visiting him. Colloquially, these emergency charging cables are referred to as "bricks". As the name implies, emergency charging cables are not necessarily meant for everyday use. For example, remember to unwind the extension cord completely before using it for charging.
There are also, out of the history, charging stations with up to three different plugs. Triple chargers are usually for charging as fast as the car can, so they use CCS. If you use in type 2 / type 1 instead, you only charge as fast as you can with type 2 / type 1.